mfe-perceptionlisted

# Perception ## Summary **Perception** (Part I: Seeing) Chapters: 1, 2, 3 Plane Position: (-0.2, 0.2) radius 0.4 Primitives: 43 Foundational measurements and relationships. The axioms of the system — numbers, distance, angles, and the geometry of seeing. **Key Concepts:** Sine Function, Cosine Function, Real Numbers, Unit Circle, Inner Product (Dot Product) ## Key Primitives **Sine Function** (definition): The sine function sin: R -> [-1,1] is defined as the y-coordinate of the point on the unit circle at angle theta from the positive x-axis. It is periodic with period 2*pi, odd: sin(-theta) = -sin(theta). - computing vertical components of circular or oscillatory motion - modeling periodic phenomena like waves and vibrations **Cosine Function** (definition): The cosine function cos: R -> [-1,1] is defined as the x-coordinate of the point on the unit circle at angle theta. It is periodic with period 2*pi, even: cos(-theta) = cos(theta). cos(theta) = sin(theta + pi/2). - computing horizontal components of circular or oscillatory motion - finding phase relationships between periodic signals **Real Numbers** (definition): The real numbers R form a complete ordered field: closed under +, -, *, /, ordered by <, and satisfying the completeness axiom. R = Q union (R \ Q). - any calculation involving continuous quantities - measuring distances, areas, or physical quantities **Unit Circle** (definition): The unit circle is the set of points (x, y) in R^2 satisfy